The stereoselectivities of organic reactions will be investigated theoretically in order to develop reliable qualitative and quantitative techniques to predict stereoselectivities and to design useful new reagents and catalysts. The success of this work should facilitate the efficient synthesis of pharmaceutical agents and help elucidate the origins of enzyme stereospecificity. The research will focus on the stereochemistry of additions to alkenes and carbonyls, including CC bond-forming processes. Companion experimental studies will be carried out to test predictions and to facilitate refinements of computational models. The proposed research has three goals: (1) the determination of accurate transition structures of organic reactions with ab initio techniques in order to establish rules of reactivity and stereoselectivity and to determine the origins of these rules; (2) the development of practical computational models for study of stereoselectivities of reactions of large organic molecules; and (3) the creation of portable computer codes to serve as aids to synthetic chemists for the prediction of stereoselectivities. For example, we will determine the origin of stereoselectivities of epoxidations of allylic alcohols by peracids and by vanadium and titanium catalyzed reactions of peroxides. The asymmetric syntheses of epoxides with the Sharpless reagent is a paradigm of selectivities, and the modelling proposed here will permit the factors controlling stereoselectivity to be incorporated into other reagents. Similar studies will be performed on the Knowles asymmetric hydrogenation, nucleophilic additions, aldol condensations, intermolecular and intramolecular Diels-Alder cycloadditions, radical additions, and intramolecular radical cyclizations. In each case, ab initio calculations will be carried out on the parent reactions, and models based on semi-empirical methods will be used to compute relative energies of diastereomeric transition states. The methods developed in this research will be used to design new highly stereoselective reagents, catalysts, and chiral auxiliaries. Insights into the high stereospecificity exhibited by enzymes are an expected dividend of this research. Programs will be devised to serve as routine aids to synthetic chemists for the prediction of reaction stereochemistries.